Question
Use the tables to create scatterplots and determine which scatterplot shows a linear association.(1 point)
Responses
x
5.0 4.6 5.9 7.8 6.4 6.8 5.3 7.2
y
9.5 9.0 11.0 13.0 11.5 12.0 10.0 12.5
x 5.0 4.6 5.9 7.8 6.4 6.8 5.3 7.2 y 9.5 9.0 11.0 13.0 11.5 12.0 10.0 12.5
x
5.0 4.6 8.5 7.8 6.8 5.3 7.0 7.2
y
12.0 8.5 6.0 10.0 12.0 10.0 12.0 10.0
x 5.0 4.6 8.5 7.8 6.8 5.3 7.0 7.2 y 12.0 8.5 6.0 10.0 12.0 10.0 12.0 10.0
x
5.0 4.6 8.5 5.9 7.8 5.3 7.0 7.2
y
12.0 9.0 15.0 11.0 13.0 8.0 14.5 10.0
x 5.0 4.6 8.5 5.9 7.8 5.3 7.0 7.2 y 12.0 9.0 15.0 11.0 13.0 8.0 14.5 10.0
x
5.0 4.6 8.5 7.8 6.4 6.8 7.0 7.2
y
3.7 2.7 6.5 2.0 5.6 3.0 7.8 6.7
x 5.0 4.6 8.5 7.8 6.4 6.8 7.0 7.2 y 3.7 2.7 6.5 2.0 5.6 3.0 7.8 6.7
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Responses
x
5.0 4.6 5.9 7.8 6.4 6.8 5.3 7.2
y
9.5 9.0 11.0 13.0 11.5 12.0 10.0 12.5
x 5.0 4.6 5.9 7.8 6.4 6.8 5.3 7.2 y 9.5 9.0 11.0 13.0 11.5 12.0 10.0 12.5
x
5.0 4.6 8.5 7.8 6.8 5.3 7.0 7.2
y
12.0 8.5 6.0 10.0 12.0 10.0 12.0 10.0
x 5.0 4.6 8.5 7.8 6.8 5.3 7.0 7.2 y 12.0 8.5 6.0 10.0 12.0 10.0 12.0 10.0
x
5.0 4.6 8.5 5.9 7.8 5.3 7.0 7.2
y
12.0 9.0 15.0 11.0 13.0 8.0 14.5 10.0
x 5.0 4.6 8.5 5.9 7.8 5.3 7.0 7.2 y 12.0 9.0 15.0 11.0 13.0 8.0 14.5 10.0
x
5.0 4.6 8.5 7.8 6.4 6.8 7.0 7.2
y
3.7 2.7 6.5 2.0 5.6 3.0 7.8 6.7
x 5.0 4.6 8.5 7.8 6.4 6.8 7.0 7.2 y 3.7 2.7 6.5 2.0 5.6 3.0 7.8 6.7
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Answers
GPT-4o mini
To determine which scatterplot shows a linear association, let's analyze the four given data sets for \( x \) and \( y \):
1. **First Data Set**:
- \( x = [5.0, 4.6, 5.9, 7.8, 6.4, 6.8, 5.3, 7.2] \)
- \( y = [9.5, 9.0, 11.0, 13.0, 11.5, 12.0, 10.0, 12.5] \)
This data appears to show an increasing trend, suggesting a positive linear association.
2. **Second Data Set**:
- \( x = [5.0, 4.6, 8.5, 7.8, 6.8, 5.3, 7.0, 7.2] \)
- \( y = [12.0, 8.5, 6.0, 10.0, 12.0, 10.0, 12.0, 10.0] \)
The values of \( y \) do not show a clear increasing or decreasing trend. In fact, they fluctuate without any consistency, indicating no linear association.
3. **Third Data Set**:
- \( x = [5.0, 4.6, 8.5, 5.9, 7.8, 5.3, 7.0, 7.2] \)
- \( y = [12.0, 9.0, 15.0, 11.0, 13.0, 8.0, 14.5, 10.0] \)
Similar to the second set, this data does not follow a clear trend; the \( y \) values vary quite significantly with \( x \), indicating no linear association.
4. **Fourth Data Set**:
- \( x = [5.0, 4.6, 8.5, 7.8, 6.4, 6.8, 7.0, 7.2] \)
- \( y = [3.7, 2.7, 6.5, 2.0, 5.6, 3.0, 7.8, 6.7] \)
In this last data set, there's also a lack of a consistent trend among the \( y \) values as \( x \) changes, suggesting no linear association.
### Conclusion
Based on this analysis, the first data set demonstrates a clear positive linear association. The trend shows that as \( x \) increases, \( y \) also increases in a consistent manner, which is characteristic of linear relationships. The other data sets do not exhibit linear associations.
1. **First Data Set**:
- \( x = [5.0, 4.6, 5.9, 7.8, 6.4, 6.8, 5.3, 7.2] \)
- \( y = [9.5, 9.0, 11.0, 13.0, 11.5, 12.0, 10.0, 12.5] \)
This data appears to show an increasing trend, suggesting a positive linear association.
2. **Second Data Set**:
- \( x = [5.0, 4.6, 8.5, 7.8, 6.8, 5.3, 7.0, 7.2] \)
- \( y = [12.0, 8.5, 6.0, 10.0, 12.0, 10.0, 12.0, 10.0] \)
The values of \( y \) do not show a clear increasing or decreasing trend. In fact, they fluctuate without any consistency, indicating no linear association.
3. **Third Data Set**:
- \( x = [5.0, 4.6, 8.5, 5.9, 7.8, 5.3, 7.0, 7.2] \)
- \( y = [12.0, 9.0, 15.0, 11.0, 13.0, 8.0, 14.5, 10.0] \)
Similar to the second set, this data does not follow a clear trend; the \( y \) values vary quite significantly with \( x \), indicating no linear association.
4. **Fourth Data Set**:
- \( x = [5.0, 4.6, 8.5, 7.8, 6.4, 6.8, 7.0, 7.2] \)
- \( y = [3.7, 2.7, 6.5, 2.0, 5.6, 3.0, 7.8, 6.7] \)
In this last data set, there's also a lack of a consistent trend among the \( y \) values as \( x \) changes, suggesting no linear association.
### Conclusion
Based on this analysis, the first data set demonstrates a clear positive linear association. The trend shows that as \( x \) increases, \( y \) also increases in a consistent manner, which is characteristic of linear relationships. The other data sets do not exhibit linear associations.